Finite Difference Modeling of Unsteady Open-Channel Flow

Abstract Open-channel flow dynamics play a critical role in hydraulic engineering, influencing flood management, sediment transport, and water resource optimization. This study presents a numerical modeling approach to simulate unsteady flow conditions in open channels using the finite difference method. The governing Saint-Venant equations are solved on a staggered grid framework, incorporating mass and momentum conservation principles. A Python-based implementation is developed to analyze flow evolution, utilizing an explicit time-stepping scheme while ensuring numerical stability through CFL constraints. Results demonstrate the impact of varying boundary conditions, friction coefficients, and inflow hydrographs on flow behavior. Comparative analysis highlights the influence of numerical diffusion and discretization errors on accuracy. The findings provide a scalable computational framework for real-world hydraulic applications, enabling improved flood forecasting and water system management.